[Amélioration de la conservation de la masse pour la méthode des fonctions de niveaux en éléments finis]
Dans cette Note, nous proposons un nouvel algorithme pour améliorer la conservation de la masse dans la méthode des fonctions de niveau dans un cadre éléments finis. Deux types de multiplicateurs de Lagrange sont introduits, associés respectivement à l'équation de redistanciation et à celle d'advection. Le premier est localisé au voisinage de l'interface, tandis que le second est associé à une correction globale au domaine de calcul. Les performances de la méthode proposée sont testées avec le cas test du disque de Zalesak, et nous observons que le taux de convergence par rapport au la taille des éléments du maillage est amélioré.
In this Note, a new algorithm is proposed for improving the mass conservation of the level set method in the finite element context. Two kinds of Lagrange multipliers are introduced, associated respectively to the redistancing and advection equations. The first one, is located at the vicinity of the interface, while the second one is associated to a correction that is global to the domain. The performances of the proposed method are tested on the Zalesak test case, and the convergence rate versus the element mesh size are founded to be improved.
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@article{CRMATH_2010__348_9-10_535_0,
author = {Laadhari, Aymen and Saramito, Pierre and Misbah, Chaouqi},
title = {Improving the mass conservation of the level set method in a finite element context},
journal = {Comptes Rendus. Math\'ematique},
pages = {535--540},
publisher = {Elsevier},
volume = {348},
number = {9-10},
year = {2010},
doi = {10.1016/j.crma.2010.03.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.03.011/}
}
TY - JOUR AU - Laadhari, Aymen AU - Saramito, Pierre AU - Misbah, Chaouqi TI - Improving the mass conservation of the level set method in a finite element context JO - Comptes Rendus. Mathématique PY - 2010 SP - 535 EP - 540 VL - 348 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.03.011/ DO - 10.1016/j.crma.2010.03.011 LA - en ID - CRMATH_2010__348_9-10_535_0 ER -
%0 Journal Article %A Laadhari, Aymen %A Saramito, Pierre %A Misbah, Chaouqi %T Improving the mass conservation of the level set method in a finite element context %J Comptes Rendus. Mathématique %D 2010 %P 535-540 %V 348 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.03.011/ %R 10.1016/j.crma.2010.03.011 %G en %F CRMATH_2010__348_9-10_535_0
Laadhari, Aymen; Saramito, Pierre; Misbah, Chaouqi. Improving the mass conservation of the level set method in a finite element context. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 535-540. doi : 10.1016/j.crma.2010.03.011. http://www.numdam.org/articles/10.1016/j.crma.2010.03.011/
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